1. Introduction
Sea level rise is an important consequence of the climate crisis because it induces a significant impact on human and natural systems. Scientific expeditions and studies ascertain a pattern of sea level rise at a global level [
1], regional [
2,
3], and local scale [
4] because of climate change. Potential consequences include flooding, coastal erosion, saltwater intrusion into low-lying aquifers, and the submergence of flat regions. Therefore, the monitoring and prediction of sea level change is a key element to sustainable planning of life in coastal regions [
5,
6,
7,
8,
9,
10]. However, in addition to contributing to climate change monitoring, sea level studies serve fundamental geosciences. Particularly, they provide the basis for the definition of height reference systems in geodesy [
11,
12,
13], assist the investigation of vertical land motion [
14,
15], and overly, provide the infrastructure for maritime spatial planning [
16].
Sea level variation is driven by a multitude of natural processes that vary both in spatial and temporal scale. In this regard, astronomical tide is a periodic phenomenon affecting sea level oscillation in a rather consistent way realized either on a day or half-day basis. Its amplitude depends primarily on geographic location featuring a temporal variation governed by the time of the day, the season of the year, and the Earth’s location in relation to the moon and the sun [
17,
18].
On the other hand, atmospheric force reflects the combined effect of air pressure and wind on sea level variation. Atmospheric effects usually last from hours to several days [
19] before they gradually relent or migrate to another spot. Although meteorological tide (also known as storm surge) reflects the atmospheric contribution on sea level variation, it is sometimes treated or meant to be simply part of the sea level residuals that remain after subtracting the effect of the astronomical tide from sea level raw observables. However, according to the literature [
17,
20,
21] and the analyses by the Intergovernmental Oceanographic Committee [
22], the storm surge comprises an individual component of sea level variation rather than a residual value alone.
Sea level monitoring is usually realized locally using tide gauge recordings acquired at selected observation sites. Studies of sea level variation can also be undertaken on the open sea or the oceans using advanced propagation models relying on seashore information in conjunction with satellite altimetry. The monitoring and analysis of sea level variation have been studied extensively in the past; for instance, see [
23,
24,
25,
26,
27,
28,
29,
30]. These studies combine records from various sources including tide gauge stations, current meters, meteorological stations, and, in certain cases, satellite altimetry. However, historically, the backbone of sea level studies relies on data derived from tide gauges and meteorological stations of various types.
This paper provides a methodological approach for sea level estimation at a single site. Firstly, the astronomical effects that mainly govern sea level fluctuations are calculated, and secondly, tidal residuals are modeled considering the meteorological force effects. The proposed strategy takes into account an evaluation process comparing tide gauge data and the result of sea level modeling. The remaining residuals are partly ascribed to the presence and amplitude of skew surges. An analysis is undertaken in Thermaikos Gulf (north Greece) using historical tide gauge data obtained from the Thessaloniki harbor station spanning a period of 21 consecutive years. Meteorological data originate from the Thessaloniki National Airport weather station. Sea level information is distinguished by its astronomical and meteorological components [
17]. Its variation is quantified through the amplitude and phase of tide constituents representing the astronomical tide on one hand and the atmospheric pressure and wind velocity for the storm surges on the other hand. Analyses yield conclusions about the tidal behavior of Thermaikos Gulf, indicating a suitable methodology for studying other areas of interest with similar characteristics.
This paper is structured as follows.
Section 2 provides some insight into the theoretical background underlying this study and describes the study area and the available data in the tide gauge and the meteorological data located in Thermaikos Gulf.
Section 3 presents, in detail, the implementation of the adopted modeling process and its associated evaluation procedure and metrics. Finally,
Section 4 provides a discussion and conclusions on the main findings and perspectives of this study.
4. Discussion
Astronomical tide approximates most sea level signals, but considerable residuals remain. These should be further modeled by addressing the meteorological effects on sea level. This paper presents a unified approach including the software tools and assessment results of coastal sea level estimation considering the full range of astronomical and meteorological tide effects. Prior to tidal model analysis, the theoretical background concerned with sea level estimation is detailed. The computational steps contributing to tidal and meteorological analysis should account for all key elements and processes (i.e., tide gauge observations, meteorological data, quality control, area geometry, harmonic analysis, and prediction model) affecting sea level estimation. As a result, the workflow introduced in
Section 2.3 has a global character. Additionally, the model adopted accounts for storm surges, and, therefore, it is particularly suited for regions with large tidal and/or meteorological variations.
The proposed methodology follows an analytical approach for sea level estimation at a single site. Implementing the equations of the model presented in this study, the physical phenomena that contribute to sea level formation can be justified to a certain extent. Model implementation revealed its correctness and operational efficiency. From another perspective, numerical analysis methodology could be followed for the same subject. An extended time series of data and the complicated hydrodynamics of wider areas could involve such techniques. Machine learning methodologies for the manipulation of extensive time series such as tide gauges, meteorological data, and meshed grids for storm surge propagation seem to be suitable when implementing a network of stations and a broad area for investigation. In this context, numerical techniques, such as those discussed earlier, should be implemented in future studies targeting a wider area of research comprising more station data. On the other hand, analytical methods in this study could evaluate the results of numerical approaches.
The assessment of the proposed method was undertaken using historical data obtained from the tide gauge and meteorological stations located in the city of Thessaloniki, Greece. Detailed analysis of the results revealed several conclusions pertaining to the observation site and the greater area. Firstly, as expected, residuals obtain lower values when storm surge modeling is considered. This conclusion agrees with the statistical metrics shown in
Table 9 and
Table 10, resulting in a satisfactory agreement between the sea level model and corresponding observed values.
However, even though residuals exhibit a small mean value (i.e., below cm level), their variance suggests inconsistencies in instrumental performance. Also, the analysis does not account for sea current information, as not enough data (i.e., dense and reliable) were available. Furthermore, it is pointed out that three rivers flow into the Thermaikos basin. The Axios, Loudias, and Aliakmonas rivers end up in the study area, no further than 30 km away from the Thessaloniki port. Clearly, this affects sea water salinity and current flows, and by extension impacts the variance of tide residuals and their average value. In this context, skew surges, despite their amplitude, exhibit a significant time shift between high tide and the maximum that is observable, which also sums up the residual values.
Considering the peculiar coastline morphology of Thermaikos Gulf (
Figure 2 and
Figure 3), we assumed alternative extents (i.e., regions) for studying the effect of storm surges in our analysis. Residual analysis (based on Willmott Skill factor results) has indicated that Saloniki Bay is very constrained, and, therefore, the whole extent of Thermaikos Gulf should be considered responsible for the storm surges that arrive at the Thessaloniki port. Obviously, depending on the study scale, one would argue that Thermaikos Gulf (
Figure 3) is still a closed system [
37]. Instead, a much broader extent could be used, such as the north Aegean region or even the entire Aegean Sea; however, this assumption necessitates adopting a different approach considering a network of tide gauge stations. In this study, this is irrelevant, as we consider only a single tide gauge point at the Thessaloniki port.
In Thermaikos Gulf, which has a considerable length of 170 km, meteorological and atmospheric conditions exhibit spatial variation. To achieve higher accuracy in storm surge estimation, the best practice would be to use a meteorological model grid, especially when the underlying effects are large enough. This study proves that sea level recorded by a tide gauge at a single point can be modeled with sufficient accuracy, even though influences originate 170 km away, considering this extent constitutes a close system.
The sea level ranges over 0.8 m for the study period and site (
Table 2). As astronomical tide dominates in the total signal, tide prediction has a considerable effect on navigating alongshore and port safety. Harbor and coastal approaches are influenced by sea level. In that context, tide prediction provides the appropriate information for safety in navigation combined with individual ship characteristics. Additionally, the highest highs and the lowest lows are significant values for port establishment and relative infrastructure designs.
In the timespan studied, extreme storm surges over 0.15 m coincide mostly with average sea level observations. Hazardous situations, such as flooding, can occur when both storm surges and tide level exhibit their extremes at the same time. In such circumstances, the sea level behavior and analysis before flooding constitute a crucial parameter as an alarm for hazard prediction. In this regard, the tidal model discussed in this study contributes toward hazard prediction by computing separated sea level components and combining them into a global estimate. Extreme storm surge values have not been extensively studied, as this aspect deviates from the central goal of the current research. Sparse occurrences in the time series of the total sea level signal indicated that there is a need for future investigation of their correlation with other sea level components. An interesting extension of this point would be studying their spatial distribution and correlation, leading to a more comprehensive spatio-temporal analysis of sea level components. This analysis would be helpful in servicing an insight into climate change and its effects on sea level variation, together with coastal design infrastructure at both engineering [
52,
53] and environmental [
8,
37] levels.
Regarding the study period, four storm events exhibited surges of some decimeters. In these extreme events, tidal prediction becomes crucial, as it will lead to total sea level estimation. High tidal levels combined with extreme storm surges can lead to flooding at nearby shores. In this regard, high sea levels from astronomical tide predictions paired with weather forecasts accounting for extreme storm surges could trigger alarms for the civil protection of near-shore dwellers.
As a general conclusion, the astronomical tide at the Thessaloniki station is low, and storm surges are even lower. Of course, some extreme values exist and are pointed out. Model residuals, despite their standard deviation values, indicate a small mean value, suggesting a good performance of the model adopted. Also, Willmott Skill and Nash–Sutcliffe efficiency show improved results when storm surges are included in the computations. In conclusion, it is apparent that storm surges contribute significantly to sea level estimation, even if they are low. Therefore, astronomical tide prediction combined with storm surge components can lead to a more accurate sea level estimation. Extreme storm surge events occurring simultaneously with extreme tidal levels could have dangerous consequences for coastal areas. Various damage and even the loss of lives are known in many regions because of that interaction. Recently, the sea level rise observed due to climate change would strengthen this effect, indicating that coastal areas are becoming even more vulnerable. Moreover, storm surges augmented by wave propagation modeling can affect coastal structure design in order to avoid flooding [
54].
In reverse, the studies of sea level estimation contribute to climate change studies. Evidently, climate change is responsible for various natural disasters occurring at a global scale, and sea level monitoring is a key parameter contributing to climate change studies. Therefore, consistent analysis and the accurate prediction of sea level variation are key aspects in the design and setup of early warning notes of such phenomena. Additionally, sea level studies contribute to various scientific purposes. Geodesy encompasses sea level studies, as they contribute to height systems and geoid determinations [
55,
56]. Moreover, accurate determination of tidal signal is critical for satellite altimetry calibration and precise tidal loading estimation for GNSS stations.
Time is a crucial parameter at all scales, and temporal variation is expressed either by the discrete values visualizing a phenomenon (time series) or by a compact function of time (formula). In this study, mean sea level was considered as a constant, which gives it the character of a bias to sea level fluctuations by tide and meteorological conditions. The linear trend added is a rough time-varying parameter. Future analyses should estimate a function for MSL, engaging time as a variable. Under this assumption, MSL stands for the low-frequency signal, astronomical tide is the intermediate one, and storm surge represents the high-frequency part of the total sea level signal. Contrarily, MSL could also be studied at a macroscale level to reveal long-term effects. This also leads to investigating the contributing factors of climate change.